It has repeatedly been shown that properly constructed monetary aggregates based on index number theory (such as Divisia money) vastly outperform traditional measures of money (i.e. simple sum money) in empirical models. However, opponents of Divisia frequently claim that Divisia is “too complex” for little gain. And indeed, at first glance it looks as if simple sum and Divisia sum exhibit similar dynamics. In this paper, we want to build deeper understanding of how and when Divisia and simple sum differ empirically using monthly US data from 1990M1 to 2007M12. In particular, we look at how they respond differently to monetary policy shocks, which seems to be the most essential aspect of those differences from the perspective of the policy maker. We use a very rich, fairly agnostic setup that allows us to identify many potential nonlinearities, building on a smoothed local projections approach with automatic selection of the relevant interaction terms. We find, that—while the direction of change is often similar—the precise dynamics differ sharply. In particular in times of economic uncertainty, when the proper assessment of monetary policy is most relevant, those existing differences are drastically augmented.

While credit cards provide transactions services, as do currency and demand deposits, credit cards have never been included in measures of the money supply. The reason is accounting conventions, which do not permit adding liabilities, such as credit card balances, to assets, such as money. However, economic aggregation theory and index number theory measure service flows and are based on microeconomic theory, not accounting. Barnett et al. derived the aggregation and index number theory needed to measure the joint services of credit cards and money. They derived and applied the theory under the assumption of risk neutrality. But since credit card interest rates are high and volatile, risk aversion may not be negligible. We extend the theory by removing the assumption of risk neutrality to permit risk aversion in the decision of the representative consumer.

In this paper we investigate the relationship between money growth uncertainty and the level of economic activity in the United States. We pay explicit attention to the Divisia monetary aggregates. In doing so, we use the new vintage of the data [called MSI (monetary services indices) by the St. Louis Fed], together with the simple sum monetary aggregates, over the period from 1967:1 to 2011:3. In the context of a bivariate VARMA, GARCH-in-mean, asymmetric BEKK model, we show that increased Divisia money growth volatility (irrespective of the level of aggregation and the method of calculation) is associated with a lower average growth rate of real economic activity. However, there are no effects of simple-sum money growth volatility on real economic activity, except with the Sum M1 and perhaps Sum M2M aggregates. We conclude that monetary policies that focus on the Divisia monetary aggregates and target their growth rates will contribute to higher overall economic growth.

This paper compares the different dynamics of the simple-sum monetary aggregates and the Divisia monetary aggregate indices over time, over the business cycle, and across high and low inflation and interest-rate phases. Although traditional comparisons of the series sometimes suggest that simple-sum and Divisia monetary aggregates share similar dynamics, there are important differences around turning points that cannot be evaluated by their average behavior. We use a factor model with a regime-switching model that separates the common movements underlying the monetary aggregate indices from idiosyncratic variations in each series. We find that the major differences between the simple-sum aggregates and Divisia indices occur around the beginnings and ends of recessions and during some high-interest-rate phases. We note the inferences' policy relevance, which is particularly dramatic at the broadest (M3) level of aggregation. Indeed, as Belongia [Journal of Political Economy, 104 (5) (1996), 1065–1083] has observed in this regard, “measurement matters.”

In this article we use Bayesian classification and finite mixture models to extract information from the MSI database (maintained by the Federal Reserve Bank of St. Louis) and construct a new set of non-nested monetary aggregates (under the Divisia aggregation procedure) based on statistical similarities and multidimensional structures. We also use recent advances in the fields of applied econometrics, dynamical systems theory, and statistical physics to investigate the relationship between the new money measures and economic activity. The empirical results offer practical evidence in favor of this approach to monetary aggregation.

Weak separability is a key admissibility property in the Divisia approach to monetary aggregation. We test groups of U.K. household sector monetary assets for weak separability using new data underlying the Bank of England's benchmark revision of its household sector Divisia index. Nonparametric tests are used to identify four monetary asset groupings, which are weakly separable over all or almost all of the post-ERM period (1992:4–2005:1). We construct Divisia monetary aggregates for these four groupings and investigate their information content in two applications. The main findings are that Divisia money has direct effects on aggregate demand and that the growth rates of the nominal Divisia monetary aggregates Granger cause nominal output growth, but not inflation.

In aggregation theory, index numbers are judged relative to their ability to track the exact aggregator functions nested within the economy's structure. We compare two statistical index numbers—the Divisia monetary aggregate and the simple-sum monetary aggregate—with the exact rational expectations monetary aggregate, using actual data. Because we are not using simulated data, we estimate the parameters of the Euler equations, and thereby of the nested monetary aggregator function, using the generalized method of moments. We explore the tracking errors of the two index numbers relative to the estimated exact aggregate. We investigate the circumstances under which risk aversion increases tracking error. We also use polyspectral methods to test for the existence of remaining nonlinear structure in the residual tracking errors.